# correct_matrix_mvrr: Multivariate select/correction for covariance matrices In psychmeta: Psychometric Meta-Analysis Toolkit

 correct_matrix_mvrr R Documentation

## Multivariate select/correction for covariance matrices

### Description

Correct (or select upon) a covariance matrix using the Pearson-Aitken-Lawley multivariate selection theorem.

### Usage

```correct_matrix_mvrr(
Sigma_i,
Sigma_xx_a,
x_col,
y_col = NULL,
standardize = FALSE,
var_names = NULL
)
```

### Arguments

 `Sigma_i` The complete range-restricted (unrestricted) covariance matrix to be corrected (selected upon). `Sigma_xx_a` The matrix of unrestricted (range-restricted) covariances among of selection variables. `x_col` The row/column indices of the variables in `Sigma_i` that correspond, in order, to the variables in `Sigma_xx_a`. `y_col` Optional: The variables in `Sigma_i` not listed in `x_col` that are to be manipuated by the multivariate range-restriction formula. `standardize` Should the function's output matrix be returned in standardized form (`TRUE`) or in unstandardized form (`FALSE`; the default). `var_names` Optional vector of names for the variables in `Sigma_i`, in order of appearance in the matrix.

### Value

A matrix that has been manipulated by the multivariate range-restriction formula.

### References

Aitken, A. C. (1934). Note on selection from a multivariate normal population. Proceedings of the Edinburgh Mathematical Society (Series 2), 4(2), 106–110.

Lawley, D. N. (1943). A note on Karl Pearson’s selection formulae. Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences, 62(1), 28–30.

### Examples

```Sigma_i <- reshape_vec2mat(cov = .2, var = .8, order = 4)
Sigma_xx_a <- reshape_vec2mat(cov = .5, order = 2)
correct_matrix_mvrr(Sigma_i = Sigma_i, Sigma_xx_a = Sigma_xx_a, x_col = 1:2, standardize = TRUE)
```

psychmeta documentation built on Aug. 26, 2022, 5:14 p.m.